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Linear Functions

SAT Math· difficulty 4/5

For f(x)=3x+af(x) = 3x + a and g(x)=bx−2g(x) = bx - 2, the composition f(g(x))=6x+1f(g(x)) = 6x + 1. What is a+ba + b?

  • A

    99

    check_circle
  • B

    1111

  • C

    77

  • D

    55

Explanation

f(g(x))=3(bx−2)+a=3bx+a−6f(g(x)) = 3(bx - 2) + a = 3bx + a - 6. Match: 3b=63b = 6 so b=2b = 2; a−6=1a - 6 = 1 so a=7a = 7. a+b=9a + b = 9.

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