Correct each of the following incorrect statements:
1)The inverse of the function defined by y= 5/x +1 is defined by y= 5/x - 1.
2)The graph of a function and its inverse are always reflection in the line =0.
To correct each of the statements, we need to carefully analyze them. Let's go through each one:
1) The inverse of the function defined by y = 5/x + 1 is defined by y = 5/x - 1.
To find the correct inverse, we need to switch the roles of x and y and solve for y again. Here's how we do it:
Start with the original function: y = 5/x + 1
Step 1: Swap x and y: x = 5/y + 1
Step 2: Solve for y: Subtract 1 from both sides and rearrange the equation:
x - 1 = 5/y
y = 5/(x - 1)
So, the correct inverse of the function is y = 5/(x - 1), not y = 5/x - 1.
2) The graph of a function and its inverse are always reflections in the line y = 0.
This statement is not accurate. The graph of a function and its inverse are reflections, but not always in the line y = 0. The line with which the graphs reflect depends on the specific function.
To find the line of reflection, we use the equation y = x. The graph of a function and its inverse are reflections across this line.
So, to correct the statement: The graph of a function and its inverse are always reflections in the line y = x, not y = 0.
By understanding the correct approach, we have now corrected the incorrect statements.