91Ó°ÊÓ

Graph each function. $$f(x)=-3(x-2)^{2}+1$$

Given functions \(f\) and \(g,\) find ( \(a\) ) \((f \circ g)(x)\) and its domain, and ( \(b\) ) \((g \circ f)(x)\) and its domain. See Examples 6 and 7 . $$f(x)=8 x+12, \quad g(x)=3 x-1$$

An equation that defines \(y\) as a function of \(x\) is given. (a) Solve for \(y\) in terms of \(x\) and $$\text {replace \(y\) with the function notation } f(x) . \text { (b) Find } f(3)$$. $$x-4 y=8$$

Use a graphing calculator to solve each linear equation. $$3(2 x+1)-2(x-2)=5$$

Use a graphing calculator to solve each linear equation. $$4 x-3(4-2 x)=2(x-3)+6 x+2$$

Given functions \(f\) and \(g,\) find ( \(a\) ) \((f \circ g)(x)\) and its domain, and ( \(b\) ) \((g \circ f)(x)\) and its domain. See Examples 6 and 7 . $$f(x)=\sqrt{x}, \quad g(x)=x+3$$

An equation that defines \(y\) as a function of \(x\) is given. (a) Solve for \(y\) in terms of \(x\) and $$\text {replace \(y\) with the function notation } f(x) . \text { (b) Find } f(3)$$. $$y+2 x^{2}=3-x$$

Given functions \(f\) and \(g,\) find ( \(a\) ) \((f \circ g)(x)\) and its domain, and ( \(b\) ) \((g \circ f)(x)\) and its domain. See Examples 6 and 7 . $$f(x)=\sqrt{x}, \quad g(x)=x-1$$

An equation that defines \(y\) as a function of \(x\) is given. (a) Solve for \(y\) in terms of \(x\) and $$\text {replace \(y\) with the function notation } f(x) . \text { (b) Find } f(3)$$. $$y-3 x^{2}=2+x$$

An equation that defines \(y\) as a function of \(x\) is given. (a) Solve for \(y\) in terms of \(x\) and $$\text {replace \(y\) with the function notation } f(x) . \text { (b) Find } f(3)$$. $$4 x-3 y=8$$