sat suite question viewer
Algebra
/ Linear functions
Difficulty: Hard
The functions and are defined as and . If the function is defined as , what is the x-coordinate of the x-intercept of the graph of in the xy-plane?
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Explanation
The correct answer is . It's given that the functions and are defined as and . If the function is defined as , then substituting for and for in this function yields . This can be rewritten as , or . The x-intercept of a graph in the xy-plane is the point on the graph where . The equation representing the graph of is . Substituting for in this equation yields . Subtracting from both sides of this equation yields , or . Therefore, the x-coordinate of the x-intercept of the graph of in the xy-plane is .