Question

0/1 Points] DETAILS Write the inverse for the function f(x) = 8x + 3 x(f) = x - 8 3 x Need Help? Read It [0/1 Points] DETAILS F Write the inverse for the function. h(t) = 0.3 + 1 t=0 0.2t,t(h) = 5 t-0.3 X

Answer 1

To find the inverse of a function, we need to interchange the roles of the dependent and independent variables and solve for the new dependent variable.

1. Inverse of f(x) = 8x + 3:

Let y = 8x + 3

To find the inverse, we swap x and y:

x = 8y + 3

Now, solve for y:

x - 3 = 8y

y = (x - 3)/8

Therefore, the inverse of f(x) = 8x + 3 is f^(-1)(x) = (x - 3)/8.

2. Inverse of h(t) = 0.3 + 1/(0.2t):

Let y = 0.3 + 1/(0.2t)

To find the inverse, we swap t and y:

t = 0.3 + 1/(0.2y)

Now, solve for y:

0.2y = t - 0.3

y = (t - 0.3)/0.2

Therefore, the inverse of h(t) = 0.3 + 1/(0.2t) is h^(-1)(t) = (t - 0.3)/0.2.

Explanation: