When Let f (x) = x^2 – 3x + 8 and
g(x) = x – 5
Find
Find the composite function of (fºg)(x) and simplify
Find (fºg)(2)
Find the composite function (gºf)(x)
To find the composite function (fºg)(x), you need to evaluate f(g(x)), which means you will substitute the function g(x) into the function f(x).
1. Begin with the function g(x) = x - 5.
2. Substitute g(x) into the function f(x): f(g(x)) = (x - 5)^2 - 3(x - 5) + 8.
3. Simplify the expression by expanding and combining like terms if necessary.
To find (fºg)(2), you need to substitute the value of x with 2 in the composite function (fºg)(x).
1. Start with the composite function f(g(x)): f(g(2)).
2. Evaluate g(2) by substituting x with 2 in the function g(x): g(2) = 2 - 5 = -3.
3. Substitute the value obtained in the previous step into the function f(x): f(-3).
4. Calculate f(-3) by substituting x with -3 in the function f(x): f(-3) = (-3)^2 - 3(-3) + 8.
5. Simplify the expression to get the final result.
To find the composite function (gºf)(x), you need to evaluate g(f(x)), which means you will substitute the function f(x) into the function g(x).
1. Begin with the function f(x) = x^2 - 3x + 8.
2. Substitute f(x) into the function g(x): g(f(x)) = f(x) - 5.
3. Simplify the expression by replacing f(x) with x^2 - 3x + 8.
By following these steps, you will be able to find the composite functions (fºg)(x) and (gºf)(x) for the given functions f(x) and g(x).