Questions: For f(x)=5x-3 and g(x)=2x^2-5, find the following functions. a. (f∘g)(x); b. (g∘f)(x); c. (f∘g)(2); d. (g∘f)(2) a. (f∘g)(x)=10x^2-28 (Simplify your answer.) b. (g∘f)(x)=50x^2-60x+13 (Simplify your answer.) c. (f∘g)(2)=12 (Simplify your answer.) d. (g∘f)(2)= (Simplify your answer.)

For f(x)=5x-3 and g(x)=2x^2-5, find the following functions.
a. (f∘g)(x); b. (g∘f)(x); c. (f∘g)(2); d. (g∘f)(2)
a. (f∘g)(x)=10x^2-28 (Simplify your answer.)
b. (g∘f)(x)=50x^2-60x+13 (Simplify your answer.)
c. (f∘g)(2)=12 (Simplify your answer.)
d. (g∘f)(2)= (Simplify your answer.)

Transcript text: For $f(x)=5 x-3$ and $g(x)=2 x^{2}-5$, find the following functions. a. $(f \circ g)(x) ;$ b. $(g \circ f)(x) ;$ c. $(f \circ g)(2) ; d .(g \circ f)(2)$ a. $(f \circ g)(x)=10 x^{2}-28$ (Simplify your answer.) b. $(g \circ f)(x)=50 x^{2}-60 x+13$ (Simplify your answer.) c. $(f \circ g)(2)=12$ (Simplify your answer.) d. $(g \circ f)(2)=$ $\square$ (Simplify your answer.)

Solution

Solution Steps

Step 1: Find the composite function (f o g)(x)

To find $(f \circ g)(x)$, we substitute $g(x) = 2_x^2-5$ into $f(x) = 5_x-3$. This gives us $(f \circ g)(x) = 5_(2_x^2-5)-3$. Evaluating this at $x = 2$, we get $(f \circ g)(2) = 12$.

Step 2: Find the composite function (g o f)(x)

To find $(g \circ f)(x)$, we substitute $f(x) = 5_x-3$ into $g(x) = 2_x^2-5$. This gives us $(g \circ f)(x) = 2_(5_x-3)^2-5$. Evaluating this at $x = 2$, we get $(g \circ f)(2) = 93$.