How do I solve for gfh
2 answers:
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Identify the vertex, axis of symmetry, minimum or maximum, domain, and range of the function ()=−(+)^−
<em><u>Answer:</u></em>
vertex = (-4, -5)
Axis of symmetry = -4
use the (-4, -5) to find the minimum value
<em><u>Solution:</u></em>
Given function is:
The equation in vertex form is given as:
Where, (h, k) is constant
On comparing give function with vertex form,
h = -4
k = -5
Vertex is (-4 , -5)
Axis of symmetry : x co-ordinate of vertex
Thus, axis of symmetry = -4
The coefficient of x^2 is positive in given function.
Thus the vertex point will be a minimum
On comparing,
a = 1
b = 8
Thus, use the (-4, -5) to find the minimum value
Domain and range
The domain is the input values shown on the x-axis
The range is the set of possible output values f(x)
Therefore,
We are given the two functions 
and 
. Since the question is asking us for the value of x when f(x) is equal to g(x), all we need to do is equate the respective expressions together. This is what the result should be:
Now, just solve for x. If you want to save some time, you can use logic and then algebra. To do this, look at the square root. We cannot have an imaginary number, so we can rule out the first two options. Now, we are left with x = 2 and x = 4. When we plug in each x-value to the equation, only 4 works out with a result of 0.5 = 0.5. Therefore, the solution to f(x) = g(x) is D) x = 4. Hope this helps and have a great day!
Now, just solve for x. If you want to save some time, you can use logic and then algebra. To do this, look at the square root. We cannot have an imaginary number, so we can rule out the first two options. Now, we are left with x = 2 and x = 4. When we plug in each x-value to the equation, only 4 works out with a result of 0.5 = 0.5. Therefore, the solution to f(x) = g(x) is D) x = 4. Hope this helps and have a great day!