Which is the inverse of the function f (x) = 1/4x + 1/2

Mathematics

1 answer:

kiruha [24]2 years ago

7 0

Answer:

f⁻¹(x) = 4x - 2

Step-by-step explanation:

To find the inverse of a function, switch the places of x and y (or f(x)).

f(x) = 1/4x + 1/2 → y = 1/4x + 1/2

Switch the variables.

x = 1/4y + 1/2

Now you want to convert the equation back into y = mx + b form.

x = 1/4y + 1/2

Subtract 1/2 from both sides.

x - 1/2 = 1/4y

Now, you want to isolate y further by dividing both sides by 1/4 (or multiplying by 4).

4(x - 1/2) = y

Distribute the 4.

4x - 2 = y → y = 4x - 2 → f⁻¹(x) = 4x - 2

This is the inverse of your given function.

You might be interested in

Find the points on the curve y = 2x3 + 3x2 − 12x + 1 where the tangent line is horizontal. (x, y) = (smaller x-value) (x, y) = (

vesna_86 [32]

Thinking about the graph of y, the rate of change is zero whenever there is an extremum.

First, differentiate y.

$y'=6x^2+6x-12$

Next, find the zeros of y' by factoring.

$6(x^2+x-2)=0 \\ x = -2, x = 1$

Now, we substitute these x-values into the original equation to find the coordinates.

$(-2,21), (1,-6)$

6 0

3 years ago

There are 4 circles and 8 squares. What is the simplest ratio of circles to total shapes?

andre [41]

Answer:

4 : 12

4/ 12

4 to 12

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers