if f(x)= 5x+7 and g(x)=x^2-2 write the functions
a. (fxg)(x)
b. f(g(x))
To find the functions (fxg)(x) and f(g(x)), we need to apply the given functions f(x) and g(x) as instructed.
a. To find (fxg)(x), we need to multiply the functions f(x) and g(x).
So, (fxg)(x) = f(x) * g(x)
Substituting the given functions:
(fxg)(x) = (5x + 7) * (x^2 - 2)
Expanding this expression by multiplying each term:
(fxg)(x) = 5x * (x^2 - 2) + 7 * (x^2 - 2)
(fxg)(x) = 5x^3 - 10x + 7x^2 - 14
Therefore, (fxg)(x) = 5x^3 + 7x^2 - 10x - 14.
b. To find f(g(x)), we need to substitute the function g(x) into f(x).
So, f(g(x)) = f(x^2 - 2)
Substituting f(x) = 5x + 7:
f(g(x)) = 5(x^2 - 2) + 7
Expanding and simplifying:
f(g(x)) = 5x^2 - 10 + 7
f(g(x)) = 5x^2 - 3
Therefore, f(g(x)) = 5x^2 - 3.