Question: User: Functions f & g are defined as f: R \to R, g:R \to R f(x)=3x+2, g(x)=5x-4 then fog is
Select one:
a. 15x+6
b. 15x-10
c. 15x-6
d. 15x+10
1. **State the problem:** We are given two functions $f(x) = 3x + 2$ and $g(x) = 5x - 4$, and we need to find the composition $f \circ g$, which means $f(g(x))$.
2. **Recall the formula for composition:** The composition $f \circ g$ is defined as $f(g(x))$, which means we substitute $g(x)$ into $f$.
3. **Calculate $f(g(x))$:**
$$f(g(x)) = f(5x - 4) = 3(5x - 4) + 2$$
4. **Simplify the expression:**
$$3(5x - 4) + 2 = 3 \times 5x - 3 \times 4 + 2 = 15x - 12 + 2$$
5. **Combine like terms:**
$$15x - 12 + 2 = 15x - 10$$
6. **Final answer:** The composition $f \circ g$ is $15x - 10$.
Therefore, the correct choice is **b. 15x-10**.