Question

What is the inverse of the function f(x) = 2x + 1? h(x) = x – h(x) = x + h(x) = x – 2 h(x) = x + 2

Answer 1

Explanation:

Start at the bit you can do...h(2)
h(x)=x2+1
h(2)=22+1 =5

Next g(x)=3x
Now we are looking at g(h(2)) but we know h(2) =5
g(5) =3*5=15
So g(h(2))=15

Next f(x) =2x-1

So similarly we are looking for f(15) =2*15=29

Answer 2

Answer:

The inverse of function is $\frac{x-1}{2}$

Step-by-step explanation:

Given the function f(x)=2x+1

Steps to find inverse functions are

Step 1: Replace f(x) with y

Step 2: Replace every x with  y and replace every y with an x

Step 3: Solve the equation from obtained in step 2 for y

Step 4: Replace y with $f^{-1}(x)$

Given function is f(x) = 2x+1

                       ⇒ y = 2x+1

Now, Replace every x with  y and replace every y with an x

⇒ x=2y+1  ⇒ 2y=x-1

                  ⇒ $y=\frac{x-1}{2}$

                  ⇒  $f^{-1}(x)=\frac{x-1}{2}$

Hence, the inverse of function is $\frac{x-1}{2}$