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spayn [35]
2 years ago
6

If f(x) = 5x+4 and g(x) = x-4, find (f o g)(x) and (g o f)(x)

Mathematics
1 answer:
Vikki [24]2 years ago
7 0

Step-by-step explanation:

F(g(x)) = F(x-4)

= 5(x-4) +4

= 5x-20+4

=5x-16

G(f(x)) = G(5x-4)

= (5x-4) -4

= 5x-8

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The table of values for the function f(x).

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The values f^{-1}(f(3.14)) and f(f(-7)).

Solution:

From the given table, it is clear that the function f(x) is defined as:

f(x)=\{(-14,11),(-7,-12),(-12,-5),(9,1),(10,-2),(-2,13)\}

We know that if (a,b) is in the function f(x), then (b,a) must be in the function f^{-1}(x). So, the inverse function is defined as:

f^{-1}(x)=\{(11,-14),(-12,-7),(-5,-12),(1,9),(-2,10),(13,-2)\}

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Using (i), we get

f^{-1}(f(3.14))=3.14

Now,

f(f(-7))=f(-12)

f(f(-7))=5

Therefore, the required values are f^{-1}(f(3.14))=3.14 and f(f(-7))=5.

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