[tex]f(x) = 7x[/tex] [tex]g(x) = \sqrt{x}[/tex] [tex]h(x) = x^2 + 7[/tex]
11)
[tex]g(f(4)) = \sqrt{7 \cdot 4} = \sqrt{28} = 2\sqrt{7}[/tex]
12)
[tex]h(g(49)) = 49 + 7 = 56[/tex]
13)
[tex]g(f(x)) = \sqrt{7x}[/tex]
14)
[tex]h(g(x)) = (\sqrt{x})^2 + 7 = x + 7[/tex]
15)
[tex](g \circ h)(x) = g(h(x)) = \sqrt{x^2 +7}[/tex]
16)
Let [tex]y = f^{-1}(x)[/tex] and [tex]f(y) = x[/tex]
[tex]4y - 3 = x\\4y = x + 3\\y = \frac{x + 3}{4}\\\\f^{-1}(x) = \frac{x + 3}{4}[/tex]
17)
Let [tex]y = g^{-1}(x)[/tex] and [tex]g(y) = x[/tex]
[tex]\frac{2y + 7}{3} = x\\ 2y + 7 = 3x\\2y = 3x - 7\\y = \frac{3x - 7}{2} \\\\g^{-1}(x) = \frac{3x - 7}{2}[/tex]
