Question

Find the inverse of the function. f(x) = 7x - 1

Answer 1

To find the inverse swap the x and y values....

f ( x) = 7x - 1 


Start by replacing f(x) by ... y 

y = 7x - 1

Now swap both x and y values....

x = 7y - 1

Solve for x...

x = 7y - 1
+1      +1

x+ 1 = 7 y

Divide both sides by 7

x/ 7 + 1/7 = y 

Now that we have our inverse you using the f(x) inverse notation..
which is ... f(x) ^-1 

So the inverse of this function is...  f(x)^-1 = x/7 + 1/7

Answer 2

The inverse of the function f(x) = 7x - 1 is $f^{-1}(x) = \frac{x}{7} + \frac{1}{7}$

The given function is:

f(x)  =  7x  -  1

Make x the subject of the formula

$f(x) = 7x - 1\\\\7x = f(x) + 1$

Divide through by 7

$\frac{7x}{7}= \frac{f(x)}{7} + \frac{1}{7}\\\\x = \frac{f(x)}{7} + \frac{1}{7}$

Replace x by $f^{-1}(x)$ and replace f(x) by x:

$f^{-1}(x) = \frac{x}{7} + \frac{1}{7}$

Therefore the inverse of the function f(x) = 7x - 1 is $f^{-1}(x) = \frac{x}{7} + \frac{1}{7}$

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