John 6:28-29
Then they asked him, “What must we do to do the works God requires?”
Jesus answered, “The work of God is this: to believe in the one he has sent.”
True: Abrahamic faith is what appropriates justification, being counted for righteousness, but Biblical faith is an obedient and repentant one. Thus (rather than reading texts in isolation) "My sheep hear my voice, and I know them, and they follow me: And I give unto them eternal life; and they shall never perish, neither shall any man pluck them out of my hand." (John 10:27-28) But that which beareth thorns and briers is rejected, and is nigh unto cursing; whose end is to be burned. But, beloved, we are persuaded better things of you, and things that accompany salvation, though we thus speak. (Hebrews 6:8-9) Thus we have promises of salvation for those who believe, as well as for those who confess and obey, as such faith is that of Abraham.
That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved. For with the heart man believeth unto righteousness; and with the mouth confession is made unto salvation. (Romans 10:9-10)
For not the hearers of the law are just before God, but the doers of the law shall be justified. (Romans 2:13)
That the righteousness of the law might be fulfilled in us, who walk not after the flesh, but after the Spirit. (Romans 8:4)
For if ye live after the flesh, ye shall die: but if ye through the Spirit do mortify the deeds of the body, ye shall live. (Romans 8:13)
And thus we see eternal life formally being given in the light of such manifest holy faith, and also exhortations to continue in the faith and warnings - to believers as believers - against failing to do so, and with chastisement in attempting to bring the wayward back to faith less they be condemned with the rest of the world.
Then shall the King say unto them on his right hand, Come, ye blessed of my Father, inherit the kingdom prepared for you from the foundation of the world: For I was an hungred, and ye gave me meat: I was thirsty, and ye gave me drink: I was a stranger, and ye took me in: (Matthew 25:34-35)
Thou hast a few names even in Sardis which have not defiled their garments; and they shall walk with me in white: for they are worthy. He that overcometh, the same shall be clothed in white raiment; and I will not blot out his name out of the book of life, but I will confess his name before my Father, and before his angels. (Revelation 3:4-5)
But Christ as a son over his own house; whose house are we, if we hold fast the confidence and the rejoicing of the hope firm unto the end. (Hebrews 3:6)
Take heed, brethren, lest there be in any of you an evil heart of unbelief, in departing from the living God. But exhort one another daily, while it is called To day; lest any of you be hardened through the deceitfulness of sin. (Hebrews 3:12-13)
For we are made partakers of Christ, if we hold the beginning of our confidence stedfast unto the end; (Hebrews 3:14)
Now the just shall live by faith: but if any man draw back, my soul shall have no pleasure in him. But we are not of them who draw back unto perdition; but of them that believe to the saving of the soul. (Hebrews 10:38-39)
For if we would judge ourselves, we should not be judged. But when we are judged, we are chastened of the Lord, that we should not be condemned with the world. (1 Corinthians 11:31-32)
Stand fast therefore in the liberty wherewith Christ hath made us free, and be not entangled again with the yoke of bondage. Behold, I Paul say unto you, that if ye be circumcised, Christ shall profit you nothing. (Galatians 5:1-2)
Christ is become of no effect unto you, whosoever of you are justified by the law; ye are fallen from grace. (Galatians 5:4)
True saving faith is characterized by obedience to Christ, and repentance when convicted of not doing so. Thus David immediately repented prayed when indicted by his own conscience via Nathan's reproof. And thus, despite his great sin, he did not become reprobate, with sin having dominion over him as Heb. 6 warns, and against which "great transgression" David prayed, "Keep back thy servant also from presumptuous sins; let them not have dominion over me: then shall I be upright, and I shall be innocent from the great transgression." (Psalms 19:13)