Question

F(x)=√2x+1 and g(x)=x-3. Find (f o g)^-1(3)​

Answer 1

To find (f o g)^-1(3), we need to first find the composition f o g, which is f(g(x)). Given f(x) = √2x+1 and g(x) = x-3, we substitute g(x) into f(x) to get (f o g)(x) = √2(x-3)+1. To find (f o g)^-1(3), we solve the equation √2(x-3)+1 = 3 for x.

Step-by-step explanation:

To find (f o g)^-1(3), we need to first find f o g. The composition f o g means we substitute the function g(x) into f(x). So, (f o g)(x) = f(g(x)). Given f(x) = √2x+1 and g(x) = x-3, we have (f o g)(x) = √2(x-3)+1.

To find (f o g)^-1(3), we need to solve the equation √2(x-3)+1 = 3 for x. Let's solve this equation step by step:

1. Subtract 1 from both sides: √2(x-3) = 2
2. Divide both sides by √2: x - 3 = 2/√2
3. Add 3 to both sides: x = 2/√2 + 3

Therefore, (f o g)^-1(3) = 2/√2 + 3.