Answer:
To find f-¹(x) of f(x) equate f(x) to y
That's
f(x) = y
So we have
[tex]y = \frac{4x - 7}{10} [/tex]
Next interchange the variables that's x becomes y and y becomes x
That's
[tex]x = \frac{4y - 7}{10} [/tex]
Next make y the subject
Cross multiply
We have
4y - 7 = 10x
Move -7 to the right side of the equation
4y = 10x + 7
Divide both sides by 4
We have the final answer as
[tex]y = \frac{10x + 7}{4} [/tex]
So
[tex]f ^{ - 1} (x) = \frac{10x + 7}{4} [/tex]
Hope this helps you