Let ( f(x) = 3x + 2 ) and ( g(x) = x^2 - 5 ). Find the composition of the functions ( (f circ g)(x) ) and ( (g circ f)(x) ).

Question

Accepted Answer

Step:1 ：First, find ( f(g(x)) ). Substituting ( g(x) ) into ( f(x) ), we get ( f(g(x)) = 3g(x) + 2 = 3(x^2 - 5) + 2 ). Simplify to get ( 3x^2 - 15 + 2 = 3x^2 - 13 ).Step:2 ：Next, find ( g(f(x)) ). Substituting ( f(x) ) into ( g(x) ), we get ( g(f(x)) = f(x)^2 - 5 = (3x + 2)^2 - 5 ). Expand and simplify to get ( 9x^2 + 12x + 4 - 5 = 9x^2 + 12x - 1 ).

Answer

Step: 1 ：First, find ( f(g(x)) ). Substituting ( g(x) ) into ( f(x) ), we get ( f(g(x)) = 3g(x) + 2 = 3(x^2 - 5) + 2 ). Simplify to get ( 3x^2 - 15 + 2 = 3x^2 - 13 ).Step: 2 ：Next, find ( g(f(x)) ). Substituting ( f(x) ) into ( g(x) ), we get ( g(f(x)) = f(x)^2 - 5 = (3x + 2)^2 - 5 ). Expand and simplify to get ( 9x^2 + 12x + 4 - 5 = 9x^2 + 12x - 1 ).

Let $f (x) = 3 x + 2$ and $g (x) = x^{2} - 5$ . Find the composition of the functions $(f \circ g) (x)$ and $(g \circ f) (x)$ .

Answer

Popular Problems

Let f(x)=3x+2 and g(x)=x2−5. Find the composition of the functions (f∘g)(x) and (g∘f)(x).

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Popular Problems

Let $f (x) = 3 x + 2$ and $g (x) = x^{2} - 5$ . Find the composition of the functions $(f \circ g) (x)$ and $(g \circ f) (x)$ .