Algebra 2/Trigonometry help?!?

x^2 = 4x

Move to the same side:

x^2 - 4x = 0

Factor out an x:

x * (x - 4) = 0

This yields two solutions:

x = 0 and x = 4

----

7sqrt(3)/2sqrt(5)

Rationalize by multiplying by sqrt(5)/sqrt(5) to get:

7sqrt(3)sqrt(5) / 2sqrt(5)sqrt(5)

Combine the roots:

7sqrt(15) / 2(5)

Simplify:

7sqrt(15) / 10

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f(x) = x + 1 and g(x) = x^2 - 1

To create the composite function, replace all x's in the g-expression with the f(x) expression:

g(f(x)) = (x + 1)^2 - 1

Expand by FOIL:

g(f(x)) = x^2 + 2x + 1 - 1

Simplify:

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

Set this equal to 0:

x^2 + 2x = 0

Factor out x:

x * (x + 2) = 0

Thus, there are two solutions:

x = 0 and x = -2

x^2 = 4x

x^2 - 4x = 0

x(x-4) = 0

x = 0 and x =4

g of f =g( f(x) )

={f(x)}^2 - 1

=(x + 1)^2 - 1

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

0 = x^2 + 2x

0 = x(x + 2 )

x = 0 or x = -2

For the first one:

x^2=4x you subtract 4x from both sides

=> x^2-4x=0 and you can then factor out an x and solve (you will get two solutions).

2nd:

I'm not sure how to interpret what you have written.

3rd:

You have f(x) = x+1,

you then plug that into g(x) to get: g(x+1) = (x+1)^2-1 and set it equal to zero.

in the first equation: divide by x. x=4

I don't really know what you meant by the second one, it wasn't really clear

g(f(x)) = (x+1)^2 - 1

(x+1) (x+1) -1 = x^2 +2x +1 -1 = x^2 +2x. Factor to get x(x + 2) = 0. x = 0, and x + 2 = 0

x = -2

x = 0