Answer to Question #94044 in Algebra for Joshua

Question

6.if \\(f(x)=2x-4)\\ and \\(g(x)= x^{2} + 3)\\, find f(g(x))
a.\\(-2x^{2} +2)\\
b.\\(-2x^{2} -2)\\
c.\\(2x^{2} -2)\\
d.\\(2x^{2} +2)\\

7.\\(f^{-1}(x)= x - 8)\\, then f(x)=?
a.x/-8
b.1/(x-8)
c.X+8
d.\\( (x-8)^{-1})\\

Answer 1

$6.\\f(x)=2x-4$

$g(x)=x^2+3$

Now,

$f(g(x))=f(x^2+3)=2(x^2+3)-4=2x^2+6-4$

$f(g(x))=2x^2+2$

Hence option (d) is correct

$7.\\f^{-1}(x)=x-8\\Let\ f^{-1}(x)=y\\So,\\f(y)=x\ \ \ \ \ \ \ \ ..... \ \ \ (1)$

$y=x-8\\x=y+8\\f(y)=y+8\\ f(x)=x+8$

So,

option (c) is correct