using the following equations, find f(g(x)): f(x)=-2x + 5 g(x)=3x - 9 f(g(x))=?x+
using the following equations, find f(g(x)): f(x)=-2x + 5 g(x)=3x - 9 f(g(x))=?x+
Answer
Explanation:
Step1: Substitute g(x) into f(x)
We know that (f(g(x))) means substituting (g(x)) into (f(x)). Since (f(x)=-2x + 5) and (g(x)=3x - 9), we replace (x) in (f(x)) with (3x - 9). So (f(g(x))=-2(3x - 9)+5).
Step2: Expand the expression
Using the distributive property (a(b - c)=ab - ac), we have (-2(3x - 9)+5=-2\times3x-2\times(-9)+5=-6x + 18+5).
Step3: Combine like - terms
Combining the constant terms (18) and (5), we get (-6x+(18 + 5)=-6x+23).
Answer:
(-6x + 23)