Chapter Closure
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Substitute the given value for x in the rule and simplify the right-hand side.
Substitute the given value for x in the rule and simplify the right-hand side.
Substitute the given value for f(x) and solve for x.
Substitute the given value for g(x) and solve for x.
f(5)=3
g(-1)=2
x=96
x=3 or x=-2
To find f(5), we have to substitute x=5 into f(x)=sqrt(x+4) and evaluate.
x= 5
Add terms
Calculate root
To find g(-1), we will substitute x=-1 in g(x)=x^2-x and evaluate.
x= (-1)
Calculate power
a-(- b)=a+b
Add terms
This time we are given the value and asked to find x when the equation equals 10. To find it, we will substitute f(x)=10 into the given rule and solve for x.
f(x)= 10
LHS-4=RHS-4
Rearrange equation
When x=96, the value of the function f(x) equals 10.
This time we are given the value and asked to find x when the equation equals 6. To find it, we will substitute g(x)=6 into the given rule and solve for x.
g(x)= 6
LHS-6=RHS-6
Rearrange equation
We got a quadratic equation in terms of only the x-terms. To solve the equation, first we should identify the values of a, b, and c.
Substitute values
The solutions for this equation are x= 1± 52. Let's separate them into the positive and negative cases.
| x=1± 5/2 | |
|---|---|
| x_1=1+5/2 | x_2=1-5/2 |
| x_1=6/2 | x_2=-4/2 |
| x_1=3 | x_2=-2 |
Using the Quadratic Formula, we found that the solutions of the given equation are x_1=3 and x_2=-2.