To find the composition of two functions, we substitute the output of the first function (f(x)) into the second function (g(x)).

Given 𝑓(𝑥)=𝑒^𝑥 and 𝑔(𝑥)=ln⁡(𝑥+5), we want to find (𝑔∘𝑓)(𝑥), which means we want to find g(f(x)).

Step 1: Find f(x), which is given as e^x.

Step 2: Substitute f(x) into g(x). So wherever we see 'x' in g(x), we replace it with f(x).

So, g(f(x)) = ln(f(x) + 5) = ln(e^x + 5).

So, (𝑔∘𝑓)(𝑥) = ln(e^x + 5).

Question

To find the composition of two functions, we substitute the output of the first function (f(x)) into the second function (g(x)).

Given 𝑓(𝑥)=𝑒^𝑥 and 𝑔(𝑥)=ln⁡(𝑥+5), we want to find (𝑔∘𝑓)(𝑥), which means we want to find g(f(x)).

Step 1: Find f(x), which is given as e^x.

Step 2: Substitute f(x) into g(x). So wherever we see 'x' in g(x), we replace it with f(x).

So, g(f(x)) = ln(f(x) + 5) = ln(e^x + 5).

So, (𝑔∘𝑓)(𝑥) = ln(e^x + 5).

Knowee AI · Accepted Answer

To find the composition of two functions, we substitute the output of the first function (f(x)) into the second function (g(x)).

Given 𝑓(𝑥)=𝑒^𝑥 and 𝑔(𝑥)=ln⁡(𝑥+5), we want to find (𝑔∘𝑓)(𝑥), which means we want to find g(f(x)).

Step 1: Find f(x), which is given as e^x.

Step 2: Substitute f(x) into g(x). So wherever we see 'x' in g(x), we replace it with f(x).

So, g(f(x)) = ln(f(x) + 5) = ln(e^x + 5).

So, (𝑔∘𝑓)(𝑥) = ln(e^x + 5).

For 𝑓(𝑥)=𝑒𝑥 and 𝑔(𝑥)=ln⁡(𝑥+5), find (𝑔∘𝑓)(𝑥)