Answer:
The solution is too long. So, I included them in the explanation
Explanation:
This question has missing details. However, I've corrected each question before solving them
Required: Determine the inverse
1:

Replace f(x) with y

Swap y & x



Divide through by 25


Replace y with f'(x)

2.

Replace g(x) with y

Swap y & x


Add 1 to both sides


Make y the subject


3:

Replace h(x) with y

Swap y & x

Add
to both sides


Multiply through by -4


Divide through by 9





4:

Replace f(x) with y

Swap y with x

Take 9th root


Replace y with f'(x)

5:

Replace f(a) with y

Swap a with y

Subtract 8


Take cube root
![\sqrt[3]{a-8} = y](https://img.qammunity.org/2021/formulas/mathematics/high-school/c2kpf3f3x42dj1q8v8uq0a0u1bl59iudnx.png)
![y = \sqrt[3]{a-8}](https://img.qammunity.org/2021/formulas/mathematics/high-school/wpcn1mbmng15d0dcyn9sdovdug4iq29ci4.png)
Replace y with f'(a)
![f'(a) = \sqrt[3]{a-8}](https://img.qammunity.org/2021/formulas/mathematics/high-school/wx8tdqr1wkddemnpd7d5ttwkllswg3s62k.png)
6:

Replace g(a) with y

Swap positions of y and a


Solve using quadratic formula:

;
;

becomes




Factorize




7:

Replace f(b) with y

Swap y and b

Open Brackets



Solve using quadratic formula:

;
;

becomes


Factorize:





Replace y with f'(b)

8:

Replace h(x) with y

Swap x and y

Cross Multiply


Subtract x from both sides:


Subtract 2y from both sides

Factorize:

Make y the subject

Replace y with h'(x)

9:

Replace h(c) with y

Swap positions of y and c

Square both sides

Subtract 2 from both sides

Make y the subject


10:

Replace f(x) with y

Swap positions of x and y

Cross Multiply


Subtract y from both sides


Add x to both sides


Factorize

Make y the subject

Replace y with f'(x)
