Answer:
Hence The composition [tex](fog)(x)[/tex] of the given function is [tex]x^2+12x+29[/tex].
Step-by-step explanation:
Given:
[tex]f(x) = x^2+2x-6[/tex]
[tex]g(x)=x+5[/tex]
We need to find [tex](f o g)(x)[/tex].
Solution:
Now we can say that;
[tex](f o g)(x)[/tex] = [tex]f(g(x))[/tex]
[tex](fog)(x) = (x+5)^2+2(x+5)-6[/tex]
Now Applying distributive property we get;
[tex](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[/tex]
Now Solving the exponent function we get;
[tex](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[/tex]
Hence The composition [tex](fog)(x)[/tex] of the given function is [tex]x^2+12x+29[/tex].
