Consider the functions 𝑔 and ℎ given by 𝑔𝑥=4𝑥 and ℎ𝑥=16𝑥+2. In the 𝑥𝑦-plane, what is the 𝑥-coordinate of the point of intersection of the graphs of 𝑔 and ℎ ?
Question
Consider the functions 𝑔 and ℎ given by 𝑔𝑥=4𝑥 and ℎ𝑥=16𝑥+2. In the 𝑥𝑦-plane, what is the 𝑥-coordinate of the point of intersection of the graphs of 𝑔 and ℎ ?
Solution
To find the x-coordinate of the point of intersection of the graphs of g and h, we need to set the two functions equal to each other and solve for x.
So, we have:
4x = 16x + 2
To solve for x, we first subtract 16x from both sides to get:
-12x = 2
Then, we divide both sides by -12 to solve for x:
x = 2 / -12
Simplifying the fraction, we get:
x = -1/6
So, the x-coordinate of the point of intersection of the graphs of g and h is -1/6.
Similar Questions
Consider the functions 𝑔 and ℎ given by 𝑔𝑥=4𝑥 and ℎ𝑥=16𝑥+2. In the 𝑥𝑦-plane, what is the 𝑥-coordinate of the point of intersection of the graphs of 𝑔 and ℎ ?Responses-4negative 4-2negative 200
Consider the functions 𝑓 and 𝑔 given by 𝑓(𝑥)=log10(𝑥-1)+log10(𝑥+3) and 𝑔(𝑥)=log10(𝑥+9). In the 𝑥𝑦-plane, what are all 𝑥-coordinates of the points of intersection of the graphs of 𝑓 and 𝑔 ?
When the quadratic function f𝑓 is graphed in the xy𝑥𝑦-plane, where y=f(x)𝑦=𝑓(𝑥), its vertex is (−4, −2)(-4, -2). One of the x𝑥-intercepts of this graph is (−274,0)(-274,0). What is the other x𝑥-intercept of the graph?(−192,0)(-192,0)eliminate(−114,0)(-114,0)eliminate(−94,0)(-94,0)eliminate(−54,0)
In the equation above, 𝑘 is a constant. One point at which the graphs of the equations intersect in the 𝑥𝑦-plane is (𝑛, 0), where 𝑛 is a constant. What is the value of 𝑘 ?
When the quadratic function f𝑓 is graphed in the xy𝑥𝑦-plane, where y=f(x)𝑦=𝑓(𝑥), its vertex is (5,3).(5,3). One of the x𝑥-intercepts of this graph is (375,0)(375,0). What is the other x𝑥-intercept of this graph?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.