TMUA Juan Set 1 Paper 1 · Question 13

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Juan Set 1 Paper 1 · Q13

Paper 1Functions & graphs

Let $a$ be a nonzero real number and $b$ , $c$ be real numbers. For the function $f$ defined on the set of real numbers by $f(x)=ax+b$ , and its inverse function $f^{-1}$ , it is given that

\lim_{x\to b}\frac{f(x)}{f^{-1}(x)}=c,\qquad f(1)=3.

What is the sum of the distinct possible values that $c$ can take?

C10

D11

E12

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