g(x)= 4−3x 8 g, left parenthesis, x, right parenthesis, equals, start fraction, 8, divided by, 4, minus, 3, x, end fraction h(y)=\dfrac{2y-9}{5}h(y)= 5 2y−9 h, left parenthesis, y, right parenthesis, equals, start fraction, 2, y, minus, 9, divided by, 5, end fraction (h\circ g) (4)=(h∘g)(4)=left parenthesis, h, circle, g, right parenthesis, left parenthesis, 4, right parenthesis, equals
Accepted Solution
A:
Answer:[tex](h\circ g)(4)=-\dfrac{11}{5}[/tex]Step-by-step explanation:Given: [tex]g(x)=\dfrac{8}{4-3x}[/tex][tex]h(y)=\dfrac{2y-9}{5}[/tex]To find: [tex](h\circ g)(4)[/tex]It is composite function (hog)(x) and to find the value at x=4We can write (hog)(4) as h(g(4))(hog)(4)=h(g(4))Now, we find g(4) [tex]g(4)=\dfrac{8}{4-3\cdot 4}[/tex][tex]g(4)=\dfrac{8}{4-12}[/tex][tex]g(4)=\dfrac{8}{-8}[/tex][tex]g(4)=-1[/tex]Put g(4) into h(y) [tex]h(g(4))=\dfrac{2\cdot g(4)-9}{5}[/tex][tex]h(g(4))=\dfrac{2\cdot -1-9}{5}[/tex][tex]h(g(4))=\dfrac{-2-9}{5}[/tex][tex]h(g(4))=-\dfrac{11}{5}[/tex]Hence, The value of composite function is [tex]-\dfrac{11}{5}[/tex]