Find the inverse of

Question

1) f(x) x-4/5

2) f(x) 2/x-3

3) f(x) 4/x

4) f(x) 2x^3-3

5) f(x) =x^7/2

Answer 1

(1)

The function is f(x) = x - 4/5

Let f(x) = y and solve x in terms of y.

y = x - 4/5

Add 4/5 to each side.

x = y + 4/5

Now interchange x and y.

y = x + 4/5

replace y by  .

Therefore inverse function is .

Answer 2

(2)

The function is f(x) = 2/x - 3

Let f(x) = y and solve x in terms of y.

y = 2/x - 3

Add 3 to each side.

2/x = y + 3

Multiply each side by x.

x(y + 3) = 2

Divide each side by (y+3).

x = 2/(y + 3)

Now interchange x and y.

y = 2/(x + 3)

Replace y by  .

Therefore inverse function is .

Answer 3

(3)

The function is f(x) = 4/x

Let f(x) = y and solve x in terms of y.

y =4/x

Multiply each side by x.

xy = 4

Divide each side by y.

x = 4 / y

Now interchange x and y.

y = 4 / x

Replace y by  .

Therefore inverse function is .

Answer 4

(5)

The function is f(x) = x^(7/2)

Let f(x) = y and solve x in terms of y.

y = x^(7/2)

Square on both sides.

y^2 = x^7

Take 7th root each side

x = (y)^(2/7)

Now interchange x and y.

y = (x)^(2/7)

Replace y by  .

Therefore inverse function is .

Answer 5

(4)

The function is f(x) = 2x³ - 3

Let f(x) = y and solve x in terms of y.

y = 2x³ - 3

Add 3 to each side.

y + 3 = 2x³

Divide each side by 2.

x³ = (y + 3) / 2

Take cuberoot each side

x = ((y + 3) / 2)^(1/3)

Now interchange x and y.

y = ((x + 3) / 2)^(1/3)

Replace y by  .

Therefore inverse function is .