The function $$\(\mathrm{f}\)$$ is defined for $$\(x \in \mathbb{R}\)$$ by $$\[ \mathrm{f}: x \mapsto a-2 x, \]$$ where $$\(a\)$$ is a constant. Express $$\(\mathrm{ff}(x)\)$$ and $$\(\mathrm{f}^{-1}(x)\)$$ in terms of $$\(a\)$$ and $$\(x\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No:9709_s20_qp_12 Year:2020 Question No:5(a)
Answer:
\(\mathrm{ff}(x)=a-2(a-2 x)\)
\(\mathrm{ff}(x)=4 x-a\)
\(\mathrm{f}^{-1}(x)=\frac{a-x}{2}\)
\(\mathrm{ff}(x)=4 x-a\)
\(\mathrm{f}^{-1}(x)=\frac{a-x}{2}\)
Knowledge points:
1.2.1 understand the terms function, domain, range, one-one function, inverse function and composition of functions
1.2.2 identify the range of a given function in simple cases, and find the composition of two given functions
1.2.3 determine whether or not a given function is one-one, and find the inverse of a one-one function in simple cases
Solution:
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