A function f is linear and can be written as $f(x)=ax+b$ with $a\neq0$. Its inverse is of the form $f^{-1}(x)=mx+n$ for constants m and n. It is also known that the function $h$ defined by $h(x)=f(2x-1)+f^{-1}(x)$ satisfies $h(x)=5x+7$ for every real x. Determine the values of a and b.

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a = (5±√17)/4, b = a(7+a)/(a‑1)

Igcse Model Questions Vol1 2025 Mathematics Question 5

A function f is linear and can be written as \(f(x)=ax+b\) with \(a\neq0\). Its inverse is of the form \(f^{-1}(x)=mx+n\) for constants m and n. It is also known that the function \(h\) defined by \(h(x)=f(2x-1)+f^{-1}(x)\) satisfies \(h(x)=5x+7\) for every real x. Determine the values of a and b.

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