Question

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

Answer 1

Answer:

$(h\circ g)(4)=-\dfrac{11}{5}$

Step-by-step explanation:

Given: $g(x)=\dfrac{8}{4-3x}$

$h(y)=\dfrac{2y-9}{5}$

To find: $(h\circ g)(4)$

It is composite function (hog)(x) and to find the value at x=4

We can write (hog)(4) as h(g(4))

(hog)(4)=h(g(4))

Now, we find g(4)

$g(4)=\dfrac{8}{4-3\cdot 4}$

$g(4)=\dfrac{8}{4-12}$

$g(4)=\dfrac{8}{-8}$

$g(4)=-1$

Put g(4) into h(y)

$h(g(4))=\dfrac{2\cdot g(4)-9}{5}$

$h(g(4))=\dfrac{2\cdot -1-9}{5}$

$h(g(4))=\dfrac{-2-9}{5}$

$h(g(4))=-\dfrac{11}{5}$

Hence, The value of composite function is $-\dfrac{11}{5}$