I really need help with these three questions!!!!!!

Question

 
Let f(x) = 4x – 3 and g(x) = 3x + 2. g(f(4)) = ?
 

27

41

185

53

182
 

Solve: sqrt(3x) = sqrt(4x - 7). Check to make sure that the solution is a true solution, and not "extraneous".
 

7

1

-7

7 or -7

sqrt(7)
 

Simplify: ((x^(1/2)) (y^(-1/4))) ^ -8 [Carefully write on paper, matching parentheses, before you begin.]
 

(x^(-7 1/2)) (y^(-8 1/4))

y^4 / x^2

1 / (x^4)(y^2)

x^4 / y^2

y^2 / x^4

Answer 1

Caleb, here we go!

 

1. If I tell you that g(x) = 3x - 1 and ask you for g(3), you are going to plug 3 in for every x. 

 

g(3) = 3(3) - 1 = 8

 

So it is, but twice, for your problem.

 

f(4) = 4(4) - 3 = 13

 

g(f(4)) = 3(13) + 2 = 41

 

2. If the square roots of two things are equal, then the two things are equal.

 

3x = 4x - 7

x = 7

 

sqrt(3(7)) = sqrt(4(7) - 7)

sgrt(21) = sqrt(21)

 

That works!

 

3. Remember that when we raise a power to a power, we multiply the powers. Also, a negative exponent flips the base and makes the exponent positive. For example, x^-2 = 1/x².

 

(x^1/2)^-8 = x^-4 = 1/x⁴

 

(y^-1/4)^-8 = y²

 

Multiplying the two, we end up with y²/x⁴

 

Got all that?

Answer 2

f(x) = 4x - 3

g(x) = 3x + 2

g(f(x)) = 3(4x - 3) + 2

g(f(x)) = 12x - 9 + 2

g(f(x)) = 12x - 7

g(f(4)) = 12(4) - 7

g(f(x)) = 48 - 7

g(f(x)) = 41

 

√3x = √(4x - 7)

Argument may not be negative. #2, 3 and #4 are out.

√7 would give √3(√7). No

7 gives √21 = √21

 

((x^1/2)(y^-1/4))^-8

A power to a power is the product of the powers.

x^-4y²

Answer 3

1) g(f(4))= 3(4X-3)+2

             3(4(4)-3)+2

             3(16-3)+2

             3(13)+2

              39+2

               =41

 

2) you would square both sides, and then you would be left with 3X=4X-7.  Solve for X and you get 7.

 

3)y^2/x^4

 

X^1/2^-8= X^-4

Y^-1/4^-8= Y^2  When you have an exponent to another exponent, you multiply the exponents.  (1/2)(-8) = -4,  (-1/4)(-8) = 2.  When you have a negative exponent, you change it to a fraction.  Therefore, X^-1/4 = 1/X^4

 

Leading to the answer y^2/x^4