Question

What is the inverse of the function h(x)=5/2x+4 h^{-1}(x)=

Answer 1

Step-by-step explanation:

Hello, please consider the following.

`h(x)=5/2x+4 \\\\x=(h^(-1)o})(x)=(hoh^(-1))(x)=h(h^(-1)(x))=(5)/(2h^(-1)(x)+4)\\\\<=> 2h^(-1)(x)+4=(5)/(x)\\\\<=> h^(-1)=((5)/(x)-4)/(2)\\\\<=>h^(-1)=(5-4x)/(2x)`

Thank you.

Answer 2

The inverse of the function h(x) = 5/2x + 4 is h^(-1)(x) = (2x - 8) / 5.

Step-by-step explanation:

To find the inverse of h(x), we need to swap the positions of x and h(x) and solve for x. Here's how we can do it:

Replace h(x) with y:

y = 5/2x + 4

Swap x and y:

x = 5/2y + 4

Isolate x:

Subtract 4 from both sides: x - 4 = 5/2y

Multiply both sides by 2: 2(x - 4) = 5y

Divide both sides by 5: (2x - 8) / 5 = y

Replace y back with h(x):

h^(-1)(x) = (2x - 8) / 5

Therefore, the inverse of h(x) is h^(-1)(x) = (2x - 8) / 5.