The point P(5,5) lies on the curve with equation y=f(x). Find the image of P on the curve with equation y=f(-x)
f(-x) is f(x) reflected across the y-axis, so (-5,5)
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To find the image of point P(5,5) on the curve with equation y = f(-x), we need to substitute the x-coordinate of P into the equation and calculate the corresponding y-coordinate.
Substituting x = 5 into the equation y = f(-x), we get:
y = f(-5)
So, the image of P on the curve with equation y = f(-x) is (-5, y), where y is the value of f(-5).
To find the image of point P(5,5) on the curve with equation y = f(-x), we need to substitute the x-coordinate of P, which is 5, into the equation and solve for the y-coordinate.
Given the equation y = f(-x), we can substitute x = 5:
y = f(-5)
This tells us that we need to find the value of y when x is -5. Since the point P(5,5) is on the original curve, it means that it satisfies the equation y = f(x). Therefore, the y-coordinate of P is equal to f(5).
To find the image of P on the curve y = f(-x), we need to find the y-coordinate when x is -5. We can accomplish this by plugging in -5 into the equation:
y = f(-(-5)) = f(5)
So, the image of P(5,5) on the curve with equation y = f(-x) is given by the point with coordinates (5, f(5)).