The functions $$\(\mathrm{f}\)$$ and $$\(\mathrm{g}\)$$ are defined by $$\[ \begin{aligned} & \mathrm{f}(x)=x^{2}-4 x+3 \text { for } x> c, \text { where } c \text { is a constant, } \\ & \mathrm{g}(x)=\frac{1}{x+1} \text { for } x> -1 \end{aligned} \]$$ It is now given that $$\(c=5\)$$. Find an expression for $$\(\operatorname{gf}(x)\)$$ and state the range of $$\(g f\)$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No:9709_s20_qp_13 Year:2020 Question No:9(d)
Answer:
\(\operatorname{gf}(x)=\frac{1}{(x-2)^{2}-1+1}=\frac{1}{(x-2)^{2}} \quad \mathrm{OE}\)
Range of \(\mathrm{gf}\) is \(0< \operatorname{gf}(x)< \frac{1}{9}\)
Range of \(\mathrm{gf}\) is \(0< \operatorname{gf}(x)< \frac{1}{9}\)
Knowledge points:
1.2.2 identify the range of a given function in simple cases, and find the composition of two given functions
Solution:
Download APP for more features
1. Tons of answers.
2. Smarter Al tools enhance your learning journey.
IOS
Download
Download
Android
Download
Download
Google Play
Download
Download
