Question

What is the inverse of the function h(x)=\dfrac{5}{2}x+4h(x)= 2 5 ​ x+4h, left parenthesis, x, right parenthesis, equals, start fraction, 5, divided by, 2, end fraction, x, plus, 4?\

Answer 1

Answer:

The inverse of the function h(x) is $h^{-1}(x)=\frac{2}{5}x-\frac{8}{5}$.

Step-by-step explanation:

The given function is

$h(x)=\dfrac{5}{2}x+4$

Replace h(x) by y.

$y=\dfrac{5}{2}x+4$

Interchange x and y.

$x=\dfrac{5}{2}y+4$

Subtract 4 from both sides to isolate variable y,

$x-4=\dfrac{5}{2}y$

Multiply both sides by 2.

$2x-8=5y$

Divide both sides by 5.

$\frac{2}{5}x-\frac{8}{5}=y$

Replace y by h⁻¹(x).

$h^{-1}(x)=\frac{2}{5}x-\frac{8}{5}$

Therefore the inverse of the function h(x) is $h^{-1}(x)=\frac{2}{5}x-\frac{8}{5}$.

Answer 2

Answer:

b, 3/2

Step-by-step explanation: