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Let #f(x) =7x+4# and g(x) = x-7 how do you find (fog)(x)?

Answer 1

Sadie Alexander

To find ( (f \circ g)(x) ), which is the composition of functions ( f(x) ) and ( g(x) ), follow these steps:

Replace ( x ) in ( f(x) ) with the expression for ( g(x) ): [ f(g(x)) = 7(g(x)) + 4 ]
Substitute the expression for ( g(x) ), which is ( x - 7 ), into the equation: [ f(g(x)) = 7(x - 7) + 4 ]
Simplify the expression by distributing and combining like terms: [ f(g(x)) = 7x - 49 + 4 ] [ f(g(x)) = 7x - 45 ]

Therefore, ( (f \circ g)(x) = 7x - 45 ).

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Answer 2

Sophie Adams

#(f@g)(x) = f(g(x)) = 7(g(x)) + 4 = 7(x-7) + 4#

#= 7x-49+4 = 7x-45#

It may be less confusing to use different variables in the two function definitions.

For example:

#f(y) = 7y + 4#

#g(x) = x-7#

Then it is clear that we can let #y = g(x)# to find:

#(f@g)(x) = f(g(x)) = f(y) = 7y+4#

#= 7*g(x)+4 = 7(x-7)+4 = 7x-49+4 = 7x-45#

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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.