how do i solve this problem?
f(x)=3x and g(x)=4x-3, find f[g(5)] and g[f(5)]
To solve this problem, you need to understand function composition. Function composition is the process of applying one function to the output of another function.
Let's find f[g(5)] first. This means that we need to find the value of g(5) first and then apply f to the result.
Step 1: Find g(5)
The function g(x) is defined as 4x-3. To find g(5), substitute x with 5 in the function:
g(5) = 4(5) - 3 = 20 - 3 = 17
Step 2: Apply f to the result
Now that we have the value of g(5), we can apply f(x) = 3x to it:
f[g(5)] = f(17) = 3(17) = 51
Therefore, f[g(5)] = 51.
Now, let's find g[f(5)]. This means that we need to find the value of f(5) first and then apply g to the result.
Step 1: Find f(5)
The function f(x) is defined as 3x. To find f(5), substitute x with 5 in the function:
f(5) = 3(5) = 15
Step 2: Apply g to the result
Now that we have the value of f(5), we can apply g(x) = 4x-3 to it:
g[f(5)] = g(15) = 4(15) -3 = 60 - 3 = 57
Therefore, g[f(5)] = 57.
In summary:
f[g(5)] = 51,
g[f(5)] = 57.