school
Acemy

Nonlinear Functions

SAT Math· difficulty 4/5

If f(x)=x2+1f(x) = x^2 + 1 and f(g(x))=x2−4x+5f(g(x)) = x^2 - 4x + 5, what is g(x)g(x)?

  • A

    x+2x + 2

  • B

    2x−42x - 4

  • C

    x−2x - 2

    check_circle
  • D

    x2−4x^2 - 4

Explanation

f(g(x))=g(x)2+1=x2−4x+5f(g(x)) = g(x)^2 + 1 = x^2 - 4x + 5, so g(x)2=x2−4x+4=(x−2)2g(x)^2 = x^2 - 4x + 4 = (x - 2)^2. Thus g(x)=x−2g(x) = x - 2.

Want 10 more like this — adaptive to your weak spots?

Practice 10 like thisarrow_forwardPredict my AP score

Related questions

auto_awesomeAll Toolsquestion_answerHomework Q&Amenu_bookAP & SAT PreptimelineLearn Mode