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How do you find #(fog)(x)# given #f(x)=2x^3-5x^2# and #g(x)=2x-1#?

Answer 1

Elijah Allen

#(2x-1)^2(4x-7)#

#"to evaluate" (f@g)(x)" substitute g(x) into f(x)"#

#f(color(red)(2x-1))#

#=2(color(red)(2x-1))^3-5(color(red)(2x-1))^2#

#"factor out " (2x-1)^2#

#rArr(2x-1)^2[2(2x-1)-5]#

#=(2x-1)^2(4x-7)#

#"which may be further expanded if you wish"#

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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.

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