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topjm [15]
3 years ago
12

FUNCTIONS: In the space provided, type the answer in descending order as it applies without any spaces between the letters, numb

ers, or symbols.
Type the composition (fog)(x) of the given functions:
f(x) = x^2 + 2x − 6 and g(x) = x + 5.
Mathematics
1 answer:
Aleonysh [2.5K]3 years ago
3 0

Answer:

Hence The composition (fog)(x) of the given function is x^2+12x+29.

Step-by-step explanation:

Given:

f(x) = x^2+2x-6

g(x)=x+5

We need to find (f o g)(x).

Solution:

Now we can say that;

(f o g)(x) = f(g(x))

(fog)(x) = (x+5)^2+2(x+5)-6

Now Applying distributive property we get;

(fog)(x) = (x+5)^2+2\times x+2\times5-6\\\\(fog)(x) = (x+5)^2+2x+10-6\\\\(fog)(x) = (x+5)^2+2x+4

Now Solving the exponent function we get;

(fog)(x) = x^2+2\times x\times 5+5^2+2x+4\\\\(fog)(x) = x^2+10x+25+2x+4\\\\(fog)(x) = x^2+12x+29

Hence The composition (fog)(x) of the given function is x^2+12x+29.

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