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If #f(x)=10x+3# and #g(x)=0.1x+0.3#, what is #f(g(x))#? What is #g(f(x))#? Are they inverse functions>

Answer 1

Sadie Alexander

#f(g(x))=x+6# and #g(f(x))=x+0.6#

As #f(x)=10x+3# and #g(x)=0.1x+0.3#

Hence #f(g(x))=f(0.1x+0.3)#

= #10(0.1x+0.3)+3#

= #x+3+3#

= #x+6#

and #g(f(x))=g(10x+3)#

= #0.1(10x+3)+0.3#

= #x+0.3+0.3#

= #x+0.6#

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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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If #f(x)=10x+3# and #g(x)=0.1x+0.3#, what is #f(g(x))#? What is #g(f(x))#? Are they inverse functions&gt;

If #f(x)=10x+3# and #g(x)=0.1x+0.3#, what is #f(g(x))#? What is #g(f(x))#? Are they inverse functions>