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If #f(x) = x^2 - 6# and #g(x) = 2^x - 1#, how do you find the value of #(g*f)(-3)#?

Answer 1

Lily Anderson

#(g.f)(-3)=7#

Let's write down the functions. #f(x)=x^2-6# and #g(x)=2^x-1#

Given we are to find what #(g.f)(-3)# is

Now, for any two functions, it's seen that #(g.f)(x)\impliesg(f(x))#

So, to solve this, we have to first find the value of #f(x)# at #x# and then substitute that value for #y# in #g(y)#.

#f(x)=x^2-6# is what we know. They've asked us to find it at #x=-3#. That makes it #f(-3)=(-3)^2-6=9-6=3# So #f(-3)=3#

Take it as #y# implying #y=3# We are now to substitute #y# in #g(y)=2^x-1# This means #g(3)=2^3-1#

The rest is just easy.

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Answer 2

Chloe Alexander

To find the value of ((g * f)(-3)), where (f(x) = x^2 - 6) and (g(x) = 2^x - 1), you need to first evaluate (g(-3)) and (f(-3)), then multiply the results together.

Evaluate (g(-3)): [g(-3) = 2^{-3} - 1 = \frac{1}{2^3} - 1 = \frac{1}{8} - 1 = -\frac{7}{8}]
Evaluate (f(-3)): [f(-3) = (-3)^2 - 6 = 9 - 6 = 3]
Now, multiply (g(-3)) and (f(-3)): [(g * f)(-3) = (-\frac{7}{8}) * 3 = -\frac{21}{8}]

So, the value of ((g * f)(-3)) is (-\frac{21}{8}).

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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.