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Linear Functions

SAT Math· difficulty 4/5

If f(x)=x+cf(x) = x + c and g(x)=2xg(x) = 2x, and f(g(3))=g(f(3))f(g(3)) = g(f(3)), what is cc?

  • A

    Any real number

  • B

    00

    check_circle
  • C

    Cannot be determined

  • D

    33

Explanation

f(g(3))=6+cf(g(3)) = 6 + c. g(f(3))=2(3+c)=6+2cg(f(3)) = 2(3 + c) = 6 + 2c. Equal   ⟺  c=2c  ⟺  c=0\iff c = 2c \iff c = 0.

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