Question

f(x)= 10x-5
What is the value of f-1(-4) ?​

Answer 1

Answer:

$f^{-1}(-4) = \frac{1}{10}$

Explanation:

Firstly finding $f^{-1}(x)$

So,

$f(x) = 10x-5$

Substitute $y = f(x)$

$y = 10x-5$

Exchange the values of x and y

$x = 10y-5$

Solving for y

$x = 10y-5$

Adding 5 to both sides

$10y = x+5$

Dividing both sides by 10

$y = \frac{x+5}{10}$

Replace $y = f^{-1}(x)$

$f^{-1}(x) = \frac{x+5}{10}$

For x = -4

$f^{-1}(-4) = \frac{-4+5}{10}$

$f^{-1}(-4) = \frac{1}{10}$

Answer 2

Answer:

$\frac{1}{10}$

Explanation:

f(x) = y (output)

y = 10x - 5

Switch variables.

Solve for y.

x = 10y - 5

x + 5 = 10y

x/10 + 1/2 = y

$f^{-1}(x)$ = 1/10x + 1/2

Put x as -4.

1/10(-4) + 1/2

-4/10 + 1/2

-4/10 + 5/10

= 1/10