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If #f(x)=3x# and #g(x)=4x-3#, how do you find f[g(5)] and g[f(5)]?

Answer 1

Liam Brennan

To find ( f[g(5)] ), we first evaluate ( g(5) ), then substitute the result into ( f(x) ).

[ g(5) = 4(5) - 3 = 20 - 3 = 17 ]

Now, we evaluate ( f(17) ):

[ f(17) = 3(17) = 51 ]

So, ( f[g(5)] = 51 ).

To find ( g[f(5)] ), we first evaluate ( f(5) ), then substitute the result into ( g(x) ).

[ f(5) = 3(5) = 15 ]

Now, we evaluate ( g(15) ):

[ g(15) = 4(15) - 3 = 60 - 3 = 57 ]

So, ( g[f(5)] = 57 ).

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Answer 2

James Allen

Evaluate #a = g(5)# then substitute the value of #a# for the argument #g(5)# in #f(g(5))# and evaluate #f(a)# for this argument.
(Similarly for #g(f(5))#)

#f(x)=3x##color(white)("XXXXXX")##rarr##color(white)("XXXX")##f(5) = 15#

#g(x) = 4x-3##color(white)("XXXX")##rarr##color(white)("XXXX")##g(5) = 17#

#f(g(5)) = f(17)# #color(white)("XXXX")##= 3(17) = 51#

#g(f(5) = g(15)# #color(white)("XXXX")##= 4(15) -3 = 57#

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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.