91Ó°ÊÓ

$$\text { Let } f(x)=2 x \text { and } g(x)=\frac{1}{x-3}, x \neq 0$$ (a) Find the value of (i) \((f \circ g)(5)\) and (ii) \((g \circ f)(5)\). (b) Find the function rule (expression) for (i) \((f \circ g)(x)\) and (ii) \((g \circ f)(x)\).

Sketch the graph of \(f,\) without a GDC or by plotting points, by using your knowledge of some of the basic functions shown in Figure 2.17. $$f: x \mapsto x^{2}-6$$

Assume that \(f\) is a one-to-one function. a) If \(f(2)=-5,\) what is \(f^{-1}(-5) ?\) b) If \(f^{-1}(6)=10,\) what is \(f(10) ?\)

Sketch the graph of \(f,\) without a GDC or by plotting points, by using your knowledge of some of the basic functions shown in Figure 2.17. $$f: x \mapsto(x-6)^{2}$$

$$\text { Let } f: x \mapsto 2 x-3 \text { and } g: x \mapsto 2-x^{2}$$ In a)-f), evaluate: a) $$(f \circ g)(0)$$ b) $$(g \circ f)(0)$$ c) $$(f \circ f)(4)$$ d) $$(g \circ g)(-3)$$ e) $$(f \circ g)(-1)$$ f) $$(g \circ f)(-3)$$ \(\ln g)-j\) ), find the expression: g) $$(f \circ g)(x)$$ h) $$(g \circ f)(x)$$ i) $$(f \circ f)(x)$$ j) $$(g \circ g)(x)$$

Assume that \(f\) is a one-to-one function. a) If \(f(-1)=13,\) what is \(f^{-1}(13) ?\) b) If \(f^{-1}(b)=a,\) what is \(f(a) ?\)

Sketch the graph of \(f,\) without a GDC or by plotting points, by using your knowledge of some of the basic functions shown in Figure 2.17. $$f: x \mapsto|x|+4$$

Assume that \(f\) is a one-to-one function. $$\text { If } g(x)=3 x-7, \text { what is } g^{-1}(5) ?$$

For each pair of functions,\( find \)(f \circ g)(x)\( and \)(g \circ f)(x)$ and state the domain for each. $$f(x)=x^{2}+1, g(x)=-2 x$$

Sketch the graph of \(f,\) without a GDC or by plotting points, by using your knowledge of some of the basic functions shown in Figure 2.17. $$f: x \mapsto|x+4|$$