First you plug 10 into g(x)
(10-4)
6
Next you plug in 6 into f(x)
6^2+1
36+1
=37
Hence the correct answer is Option (A) i.e. 37
The composition of a function is an operation where two functions say f and g generate a new function.
Given,
[tex]f(x)= x^2+1[/tex]-------------------(1)
and, [tex]g(x)= x-4[/tex]
Now ,
[tex]fog(x)=f[g(x)][/tex]
[tex]=f(x-4)[/tex]
[tex]=(x-4)^2+1[/tex] (from 1)
[tex]=x^2-8x+16[/tex][tex]+1[/tex]
[tex]fog(x)=x^2-8x+17[/tex]-----------------(2)
Now , we need to find [tex]fog(10)[/tex]
so, put x=10 in equation 2, we get:
[tex]fog(10) = 10^2 -8(10)+17\\fog(10) = 100-80+17\\fog(10) = 37[/tex]
Hence, the answer is 37
Learn more about Composition of Functions :
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