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How do you find [g of h](x) if #g(x)=8-2x# and #h(x)=3x#?

Answer 1

Elijah Allen

To find ( g \circ h (x) ), substitute ( h(x) ) into ( g(x) ) and simplify:

[ g \circ h(x) = g(h(x)) = g(3x) = 8 - 2(3x) = 8 - 6x ]

So, ( g \circ h(x) = 8 - 6x ).

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Answer 2

James Allen

[ g of h ]#(x) = 8-6x#

[g of h]#(x)# can be written as #g(h(x))#

Given #g(color(blue)(x)) = 8 - 2color(blue)(x)# but the #x# is just a variable place holder and we can replace it with anything we like.

So #g(color(blue)(w)) = 8 - 2color(blue)(w)# would have identical meanings as would #g(color(blue)(h(x))) = 8 -2 color(blue)(h(x)#

Using this last form and replacing color(blue)(h(x)) on the right side with its definition: #color(blue)(h(x)) = color(blue)(3x)#

We have #g(h(x)) = 8 - 2(color(blue)(3x))#

#color(white)("XXXX")= 8 - 6x#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.