Consider the functions f( x) = square root of x and g(x). =7x+ b. In the standard (x,y) coordinate plane, y = f( g ( x)) passes through (4,6). What is the value of b?

Question

Consider the functions f( x) = square root of x  and g(x). =7x+ b. In the standard (x,y) coordinate plane, y = f( g ( x)) passes through (4,6). What is the value of b?

daniel.ohearn1 · Answer

So how would you first go about writing f(g(x))?  Any ideas?

kkutie7 · Answer

$$f(x)=\sqrt{x}$$
$$g(x)=7x+b$$
it looks like you need to find the new function y

kkutie7 · Answer

same concept as this:
$$f(x)=x^{2}$$
$$x=2$$
and we need 
y=f(x)
$$y=f(x)=2^{2}=4$$

kkutie7 · Answer

you need to substitute g(x) into the function f(x). from there you need to use the coordinates to find your unknown.
once you have : $$y=f(g(x))$$
you can do this:
$$6=f(g(4))$$
tag me if you need help, but I encourage you to type what you can do in here first =)

jhonyy9 · Answer

f(x)=sqrt(x)
g(x)=7x+b

f(g(x)) = sqrt(g(x)) = sqrt(7x+b)
from y=f(g(x))  pass. trough (4,6) mean that f(g(4))=6 so
sqrt(7*4+b) = 6
sqrt(28+b) = 6 square both sides 
28+b=36
b=36-28
b=8

hope this will help you so easy understanding the way hhow you can solve it right