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CCSS.Math: ,

the graph of the function f is shown below what is the input value other than negative five for which f of X is equal to f of negative five so we have our x-axis we have our y-axis and then in blue they've graphed y equals f of X so for example when X is equal to one f of X when y is going to be equal to f of X that's what this graph is is f of X is equal to 1 when X is equal to 7 f of 7 we see is equal to 5 when X is equal to 9 we see that F of 9 is equal to 6 so what is the input value other than negative 5 for which f of X is equal to f of negative 5 so let's see if X is equal to negative 5 F of negative 5 is we move up here to the graph it is equal to 4 because this once again this is the graph y is equal to f of X so the y-coordinate here this is what f of X which is what f of negative 5 is equal to so f of negative 5 is equal to 4 so where else does that happen so let's see let's just move horizontally to the right that happens here as well so what input do we have to give what's the x coordinate here to get y is equal to f of X where f of X is equal to 4 right over here well we see the x coordinate is also 4 so this tells us that F of 4 is equal to 4 which is the same thing as F of negative 5 so when X is 4 the function takes on the same value as when X is negative 5 so x equals 4 and we're done