Question

Can you see it? Help please

Answer 1

$f(x) = 7x$          $g(x) = \sqrt{x}$          $h(x) = x^2 + 7$

11)

$g(f(4)) = \sqrt{7 \cdot 4} = \sqrt{28} = 2\sqrt{7}$

12)

$h(g(49)) = 49 + 7 = 56$

13)

$g(f(x)) = \sqrt{7x}$

14)

$h(g(x)) = (\sqrt{x})^2 + 7 = x + 7$

15)

$(g \circ h)(x) = g(h(x)) = \sqrt{x^2 +7}$

16)

Let $y = f^{-1}(x)$  and $f(y) = x$

$4y - 3 = x\\4y = x + 3\\y = \frac{x + 3}{4}\\\\f^{-1}(x) = \frac{x + 3}{4}$

17)

Let $y = g^{-1}(x)$  and $g(y) = x$

$\frac{2y + 7}{3} = x\\ 2y + 7 = 3x\\2y = 3x - 7\\y = \frac{3x - 7}{2} \\\\g^{-1}(x) = \frac{3x - 7}{2}$