If f(x)=2x-1 and g(x)=-2find [g f](x)
1 answer:
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Answer:
Answers are in bold type
Step-by-step explanation:
f(x) =
The parabola opens up, so has a minimum at the vertex.
Let (h, k) be the vertex
h = -b/2a = - (-144)/2(1) = 57
k = 57^2 - 144(57) = 3249 - 6498 = -3249
Therefore, the vertex is (57, -3249)
The minimum value is -3249
The domain is the set of real numbers.
The range = {y | y ≥ -3249}
The function decreases when -∞ < x < 57 and increases when 57 > x > ∞
The x - intercepts: = 0
x(x - 114x) = 0
x = 0 or x = 114
x-intercepts are (0, 0) and (0, 114)
When x = 0, then we get the y-intercept. So, 0^2 - 114(0) = 0
y-intercept is (0, 0)
<u>Answer:</u>
<em>The value of x in log x + log 3 = log 18 is </em><em>6</em><em>.</em>
<u>Solution:</u>
From question, given that log x + log 3 = log 18 ---- eqn 1
Let us first simplify left hand side in above equation,
We know that log m + log n = log (mn) ----- eqn 2
Adding log m and log n results in the logarithm of the product of m and n (log mn)
By using eqn 2, log x + log 3 becomes log 3x.
log x + log 3 = log 3x ---- eqn 3
By substituting eqn 3 in eqn 1, we get
log 3x = log 18
Since we have log on both sides, we can cancel log and the above equation becomes,
3x = 18
Thus the value of x in log x + log3 = log18 is 6