Final answer:
The truth of the statement 'the solution to f(x)=5 is x=4' depends on the specific function f. To verify, we must substitute x with 4 and check if the outcome is indeed 5. If the function is quadratic, solving it may require the quadratic formula.
Step-by-step explanation:
Whether the solution to f(x)=5 is x=4 depends on the form of the function f. The statement is true only if plugging x=4 into the function f results in f(4)=5. Without knowing the explicit function f(x), we cannot determine the veracity of the statement. If we are given a particular function, such as f(x) = x + 1, we can substitute x with 4 and see if f(4) = 5. Since f(4) = 4 + 1 = 5, for this particular function, the statement would be true.
However, if f(x) does not yield 5 when x is 4, the statement is false. For example, if f(x) = 2x, then f(4) = 2(4) = 8 ≠ 5, making the statement false. In such a case, to correct it, we need to find the correct value of x that satisfies f(x) = 5. This typically involves solving the equation f(x) = 5 for x. If the equation is quadratic, we may need to use the quadratic formula to find the solution for x.