How many solutions does the following equation have? 4x + 3x - 8 = 14 + 7x
1 answer:
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Answer:
x = 9,-21
Step-by-step explanation:
Given:
Transport -7 to add 8:
Cancel absolute sign and add plus-minus to 15:
Transport 6 to subtract ±15:
Consider:
or
or
Solution:
or
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Second Method
Given:
Transport -7 to add 8:
Absolute Function Property:
Consider both intervals:
When x ≥ a then:
Transport 6 to subtract 15:
When x < a then:
Transport -6 to add 15:
Transport negative sign to 21:
Solution:
or
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Let me know if you have any questions regarding this question, my answer or explanation. Hope this answer and explanation helps you and good luck with your assignment!
Let's complete the square
f(x) = x^2 + 6x + 8
y = x^2 + 6x + 8
y-8 = x^2 + 6x
y-8+9 = x^2+6x+9 .... see note below
y+1 = (x+3)^2
y = (x+3)^2-1
note: I added 9 to both sides due to taking half of the 6, and then squaring that result.
We'll restrict x such that to ensure that this function is one-to-one.
Now we need to swap x and y, and solve for y to get the inverse
y = (x+3)^2 - 1
x = (y+3)^2 - 1
x+1 = (y+3)^2
(y+3)^2 = x+1
y+3 = sqrt(x+1)
y = sqrt(x+1)-3
g(x) = sqrt(x+1)-3 is the inverse
The graph is shown below. The original function is in red. The inverse is in blue. The inverse is the result of reflecting the red curve over the dashed line y = x. So this explains why x and y swap places. Consequently, the domain and range also swap as well.
