Let for all real

MATHEMATICS · Single correct · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

Let f(x)=2x+5f(x)=2x+5 for all real xx. Find the ordered pair (a,b)(a,b) so that g(x)=ax+bg(x)=ax+b satisfies f(g(x))=xf\bigl(g(x)\bigr)=x for every real xx. (a) (12,−2)(\tfrac12,-2) (b) (12,−52)(\tfrac12,-\tfrac52) (c) (12,52)(\tfrac12,\tfrac52) (d) (2,−52)(2,-\tfrac52)

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